Angular spread between two colour light (refraction)

In summary, the question is asking for the angular spread between red and violet light in the ethanol when white light travels from crown glass. This can be found by using Snell's Law to find the angles of refraction for red and violet light in the crown glass, which then become the angles of incidence for the crown-ethanol interface. Finally, the angular separation can be calculated by finding the difference between the two angles of refraction in the ethanol.
  • #1
8uhohs
6
0
Hi, I know I've seen this question on this site before, but it didn't explain how to do it. I don't even know where to begin...

Q: Consider the optical interface between crown glass and ethanol.

b) White light travels from crown glass into ethanol. If the angle of incidence in crown
glass is 60.00 degrees, what is the angular spread between the red and violet parts of the visible spectrum in the ethanol? Illustrate your
answer with a light-ray diagram.

index of refraction:
red light in crown glass - n=1.520
violet light in crown glass - n=1.538
red light in ethanol - n=1.363
violet light in ethanol - n=1.376

I think I'm suppose to use Snell's Law...but don't know how. Thanks in advance for your help
 
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  • #2
Angle of incidence is given. find angle of refraction for red and violet color in the crown glass.

These angle of refractions become angle of incidence for the crown-ethanol interface.

Now find the angle of refraction in the ethanol for red and violet by using

n1*sinθ1 = n2*sinθ2.

Τhe angular separation = θ2 - θ1.
 
  • #3
rl.bhat said:
Angle of incidence is given. find angle of refraction for red and violet color in the crown glass.

These angle of refractions become angle of incidence for the crown-ethanol interface.

Now find the angle of refraction in the ethanol for red and violet by using

n1*sinθ1 = n2*sinθ2.

Τhe angular separation = θ2 - θ1.

do i find the angle of refraction for red and violet in the crown glass with n1*sinθ1 = n2*sinθ2 also?

here's my attempt..i think it's wrong though, because what I'm not sure w/ is what do i put for n2 in the equations...

crown glass: n=1.52
ethanol: n=1.36

red:
sinθ2=(n1*sinθ1)/n2
=(1.520)(sin60.0)/1.52(?)
θ2=60.0degrees

violet:
sinθ2=(n1*sinθ1)/n2
=(1.538)(sin60.0)/1.52
θ2=61.2degrees

then,

red:
sinθ2=(n1*sinθ1)/n2
=(1.52)(sin60.0)/1.36
θ2=75.4degrees

violet:
sinθ2=(n1*sinθ1)/n2
=(1.538)(sin61.2)/1.36
θ2=82.3degrees

Τhe angular separation = θ2 - θ1
=82.4-75.4
=7 degrees

Thank you for the help!~
 
  • #4
In the first case light is traveling from air to crown glass.

So for red light sin60 = 1.52sinθ2.

In the second case 1.52sin(θ2) = 1.36sin(θ3)

Similarly try for violet light.
 
  • #5
.

I can help you understand how to approach this problem. First, let's review the concept of refraction. Refraction is the bending of light as it passes through a medium with a different optical density. This bending is determined by the index of refraction of the two materials. Snell's Law states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the indices of refraction of the two materials.

In this case, we are dealing with two materials - crown glass and ethanol. The index of refraction for each material is given for both red and violet light. To find the angle of refraction in ethanol, we need to use Snell's Law. The equation for Snell's Law is n1sinθ1 = n2sinθ2, where n1 and n2 are the indices of refraction for the two materials and θ1 and θ2 are the angles of incidence and refraction, respectively.

To solve for the angle of refraction for red light in ethanol, we can plug in the values given: n1 = 1.520, n2 = 1.363, and θ1 = 60.00 degrees. Solving for θ2, we get θ2 = sin^-1(1.520/1.363 * sin(60.00)) = 48.92 degrees. Similarly, we can solve for the angle of refraction for violet light in ethanol, using the given values for n1, n2, and θ1. We get θ2 = sin^-1(1.538/1.376 * sin(60.00)) = 50.37 degrees.

Now, to find the angular spread between the red and violet parts of the visible spectrum in ethanol, we simply subtract the two angles of refraction: 50.37 - 48.92 = 1.45 degrees. This means that the angular spread between red and violet light in ethanol is 1.45 degrees.

To illustrate this, we can draw a light-ray diagram. Draw a horizontal line to represent the interface between crown glass and ethanol. Draw a vertical line to represent the incident ray of white light from crown glass. From the point where the incident ray hits the interface, draw two lines at the angles of refraction we calculated for red and violet light in ethanol. These lines will represent the paths of
 

1. What is angular spread?

Angular spread refers to the amount of deviation of a light ray as it passes through a medium, such as a prism or lens. It is typically measured in degrees and is caused by the refraction of light.

2. How is angular spread calculated?

Angular spread can be calculated using Snell's law, which states that the angle of incidence of a light ray is directly proportional to the angle of refraction. This can be expressed as θi / θr = n2 / n1, where θi is the angle of incidence, θr is the angle of refraction, and n1 and n2 are the refractive indices of the two media.

3. What factors affect the angular spread of light?

The angular spread of light is affected by the angle of incidence, the refractive indices of the two media, and the wavelength of light. A higher angle of incidence or a larger difference in refractive indices will result in a greater angular spread. Additionally, different wavelengths of light will experience different amounts of refraction, leading to varying angular spreads.

4. How does angular spread impact the appearance of light?

The angular spread of light can cause the separation of different wavelengths, resulting in the appearance of different colors. This is seen in rainbows, where white light is separated into its component colors due to the angular spread of light through water droplets. In other cases, the angular spread may cause distortion or blurring of images.

5. Can angular spread be controlled or manipulated?

Yes, angular spread can be controlled and manipulated using various optical devices such as lenses, prisms, and filters. These devices can alter the path of light and change the angle of incidence, resulting in different amounts of angular spread. This is the basis for many optical technologies, including cameras, telescopes, and microscopes.

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